Digital data acquisition

Sampling

When an oscilloscope samples an input signal, samples are taken at fixed intervals.
At these intervals, the size of the input signal is converted to a number.
The accuracy of this number depends on the resolution of the oscilloscope.
The higher the resolution, the smaller the voltage steps in which the
input range of the instrument is divided.
The acquired numbers can be used for various purposes, e.g. to create a graph.

The sine wave in the above picture is sampled at the dot positions.
By connecting the adjacent samples, the original signal can be reconstructed from the samples.
You can see the result in the next illustration.

Sample frequency

The rate at which samples are taken by the oscilloscope is called the sample frequency,
the number of samples per second.
A higher sample frequency corresponds to a shorter interval between the samples.
As is visible in the picture below, with a higher sample frequency,
the original signal can be reconstructed much better from the measured samples.

The sample frequency must be higher than 2 times the highest frequency in the input signal.
This is called the Nyquist frequency.
Theoretically it is possible to reconstruct the input signal with more than 2 samples per period.
In practice, at least 10 to 20 samples per period are recommended to be able to examine the
signal thoroughly in an oscilloscope.
When the sample frequency is not high enough, aliasing will occur.

Clicking the Sample frequency label in the combined Record length + Sample frequency +
Resolution indicator on the instrument toolbar and selecting the
required value from the popup menu.

Right-clicking the horizontal scrollbar under the graph displaying signals from the
instrument and selecting Sample frequency and then the appropriate value in the
popup menu.

Right-clicking the instrument in the Object Tree, selecting Sample frequency and
then the appropriate sample frequency value in the popup menu

Information:
Depending on the instrument settings, the instrument can have certain limitations with respect to the available
sample frequencies.
When a user defined value is requested that is not available, the software will use the closest available value.

Aliasing

When sampling an analog signal with a certain sampling frequency,
signals appear in the output with frequencies equal to the sum and difference of the signal frequency and multiples
of the sampling frequency.
For example, when the sampling frequency is 1000 Hz and the signal frequency is 1250 Hz,
the following signal frequencies will be present in the output data:

Multiple of sampling frequency

1250 Hz signal

-1250 Hz signal

...

-1000

-1000 + 1250 =

250

-1000 - 1250 =

-2250

0

0 + 1250 =

1250

0 - 1250 =

-1250

1000

1000 + 1250 =

2250

1000 - 1250 =

-250

2000

2000 + 1250 =

3250

2000 - 1250 =

750

...

As stated before, when sampling a signal, only frequencies lower than half the sampling frequency can be
reconstructed.
In this case the sampling frequency is 1000 Hz, so we can we only observe signals with a frequency ranging from
0 to 500 Hz.
This means that from the resulting frequencies in the table,
we can only see the 250 Hz signal in the sampled data.
This signal is called an alias of the original signal.

If the sampling frequency is lower than 2 times the frequency of the input signal, aliasing will occur.
The following illustration shows what happens.

In this picture, the green input signal (top) is a triangular signal with a frequency of 1.25 kHz.
The signal is sampled with a frequency of 1 kHz.
The corresponding sampling interval is 1/( 1000 Hz ) = 1 ms.
The positions at which the signal is sampled are depicted with the blue dots.

The red dotted signal (bottom) is the result of the reconstruction.
The period time of this triangular signal appears to be 4 ms,
which corresponds to an apparent frequency (alias) of 250 Hz (1.25 kHz - 1 kHz).

In practice, to avoid aliasing, always start measuring at the highest sampling frequency and lower the sampling
frequency if required.
Use function keys F3 (lower) and F4 (higher) to change the
sampling frequency in a quick and easy way.
The next illustration gives an example of what aliasing can look like.

In this picture, a sine wave signal with a frequency of 257 kHz is sampled at a frequency of 50 kHz.
The minimum sampling frequency for correct reconstruction is 514 kHz.
For proper analysis, the sampling frequency should have been approximately 5 MHz.

Record Length

With a given sampling frequency, the number of samples that is taken determines the duration of the measurement.
This number of samples is called record length.
Increasing the record length, will increase the total measuring time.
The result is that more of the measured signal is visible.
In the images below, three measurements are displayed, one with a record length of 12 samples,
one with 24 samples and one with 36 samples.

The total duration of a measurement can easily be calculated, using the sampling frequency and the record length:

Clicking the Record length label in the combined Record length + Sample frequency + Resolution indicator
on the instrument toolbar and selecting the required value from the popup menu.

Right-clicking the horizontal scrollbar under the graph displaying signals from the
instrument and selecting Record length and then the appropriate value in the popup menu.

Right-clicking the instrument in the Object Tree, selecting Record length and then
the appropriate value in the popup menu.

Information:
Depending on the instrument settings, the instrument can have certain limitations with respect to the available
record lengths.
When a user defined value is requested that is not available, the software will use the closest available value.

Time base

The combination of sampling frequency and record length forms the
time base of an oscilloscope.
To setup the time base properly, the total measurement duration and the required time resolution have to be taken
in account.

There are several ways to find the required time base setting.
With the required measurement duration and sampling frequency, the required number of samples can be determined:

With a known record length in samples and the required measurement duration, the necessary sampling frequency can
be calculated:

In the Multi Channel oscilloscope software, both record length and sampling frequency can be set independently, to give the best flexibility.
They can be selected from menu's, using toolbar buttons but also keyboard short cuts are available.
For more information, refer to:

Because a certain time/div setting can be created from different combinations of record length
and sampling frequency, the Multi Channel oscilloscope software must decide which combination is used.
The software will try to use the highest sample frequency possible and will adjust the record length accordingly to
obtain the required time/div setting.

To avoid the record length becoming this long that collecting the measured values takes longer resulting in the scope
responding slower, the record length for time/div settings is limited to a value that can be set in the
program settings.
When the time/div setting is adjusted by one of the corresponding controls, the maximum record length is limited
to this value.

This limit does not apply to manually adjusting the record length.

Resolution

When digitizing the samples, the voltage at each sample time is converted to a number.
This is done by comparing the voltage with a number of levels.
The resulting number is the number of the highest level that's still lower than the voltage.
The number of levels is determined by the resolution.
The higher the resolution, the more levels are available and the more accurate the
input signal can be reconstructed.
In the image below, the same signal is digitized, using three different amounts of levels:
16, 32 and 64.

The number of available levels is determined by the resolution:

The used resolutions in the previous image are respectively: 4 bits, 5 bits and 6 bits.

The smallest detectable voltage difference depends on the resolution and the input range.
This voltage can be calculated as:

In the 200 mV range, the full scale ranges from -200 mV to +200 mV, the full range is 400 mV.
When a 12 bit resolution is used, there are 212 = 4096 levels.
This results in a smallest detectable voltage step of 0.400 V / 4096 = 97.7 µV.
In 16 bit resolution this step is 0.400 V / 65536 = 6.1 µV